A041174 -id:A041174 - cp's OEIS frontend

A010168 Continued fraction for sqrt(97).

9, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18, 1, 5, 1, 1, 1, 1, 1, 1, 5, 1, 18

Offset: 0

N. J. A. Sloane

			9.848857801796104721746211414... = 9 + 1/(1 + 1/(5 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 12 2009

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,1).

Cf. A010548 (decimal expansion).

Cf. A041174/A041175 (convergents).

ContinuedFraction[Sqrt[97],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9},120,{18,1,5,1,1,1,1,1,1,5,1}] (* Harvey P. Dale, Jun 07 2016 *)

{ allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(97)); for (n=0, 20000, write("b010168.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 12 2009

A041175 Denominators of continued fraction convergents to sqrt(97).

Original entry on oeis.org

1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352, 120205801, 126583153, 753121566, 879704719, 1632826285, 2512531004, 4145357289, 6657888293, 10803245582, 60674116203, 71477361785

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1).

Cf. A041174, A010168, A020854, A010548.

I:=[1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352]; [n le 22 select I[n] else 11208*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

Denominator[Convergents[Sqrt[97], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

G.f.: -(x^20 -x^19 +6*x^18 -7*x^17 +13*x^16 -20*x^15 +33*x^14 -53*x^13 +86*x^12 -483*x^11 +569*x^10 +483*x^9 +86*x^8 +53*x^7 +33*x^6 +20*x^5 +13*x^4 +7*x^3 +6*x^2 +x +1) / (x^22 +11208*x^11 -1). - Colin Barker, Nov 14 2013

a(n) = 11208*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 12 2013

More terms from Colin Barker, Nov 14 2013

cp's OEIS Frontend

A010168 Continued fraction for sqrt(97).

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